ETH had some introductory events for the students as well as student parties almost every week that you got invitations to via email. They also had a lot of interesting entrepreneurial events that everyone could attend.
One of the things I found best about ETH was their free ASVZ gyms. Each campus of ETH as well as the University of Zurich had gyms where they also offered group trainings and everything was for free. They even organized different activities that you could attend cheaper such as for example ski trip for one day or for a week. I actually went on the ski trip for a day and met some really nice people there that I'm still friends with.
My favorite group training at the ASVZ used to be crossfit which was quite professional and it was great stress relief and just great way to spend an hour of the day. It was also a nice place to meet people since everyone basically knew each other there. You could also choose a lot of other activities such as superkondi (high intensity running, jumping and strength exercises) which was really fun, as well as yoga, martial arts, dancing, gymnastics, running, spinning and so on... They really had a lot to choose from! In the summer they even had water sports such as stand up paddling (which I've tried and it was super fun!), kayaking and so on.
On my free time, as it's probably easy to see already I did a lot of sports and hung out mostly with the friends from my WOKO and also from the lab. Since our WOKO was so big we actually had huge parties at the house which really resembled a club and the neighbors didn't live it so much but we had a lot of fun. We didn't really go out so much since we always ended up staying at home cause it was nicer. When we did go out we usually went to a bar and club street in the city called Langstrasse. It is a very interesting street which has all kinds of bars and clubs you can think of where one bar can be really fancy and another one right next to it can be really bad. So it was a bit exciting and a bit of a lottery of where you'd end up at... The ones we went though were really nice and cosy.
The city in general is sort of divided into two sides as there is a river that flows in between each side and the side with Bahnhofstrasse is in general more expensive than the other side called Niederdorf. This is true for most of the stores, restaurants and bars so if you want to go out in the city centre it's better to go out on the Niederdorf side.
There are a lot of events in Zurich such as street food festivals, open air festivals in summer, carnivals year-round and so on. It is very interesting to see how the city can change completely during such events, going from really neat-Swiss city to a loud and eventful place with not so much organization. The festivals and carnivals are usually really fun so I would recommend going to them.
There is also a mountain in Zurich called Uetliberg that you can hike up to or take a train up and enjoy the beautiful view over the whole city. It is really fun, I've hiked up there three times with different people that came to visit since it's definitely one of the must-do things in Zurich.
If you like bigger challenges I'd also recommend biking around the lake Zurich or at least a part of it. You can rent a bike at the central station for a day and just bike. I biked around the lake with some friends and it was 105 km of great adventure where you saw so much of the Swiss small towns, the different nature (as it becomes more mountains on the other side of the lake) and even got some unexpected mountain biking somewhere along the way. It was definitely one of the most fun things I did there!